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Adaptive time step selection for Spectral Deferred Correction (2403.13454v2)
Published 20 Mar 2024 in math.NA, cs.DC, and cs.NA
Abstract: Spectral Deferred Correction (SDC) is an iterative method for the numerical solution of ordinary differential equations. It works by refining the numerical solution for an initial value problem by approximately solving differential equations for the error, and can be interpreted as a preconditioned fixed-point iteration for solving the fully implicit collocation problem. We adopt techniques from embedded Runge-Kutta Methods (RKM) to SDC in order to provide a mechanism for adaptive time step size selection and thus increase computational efficiency of SDC. We propose two SDC-specific estimates of the local error that are generic and do not rely on problem specific quantities. We demonstrate a gain in efficiency over standard SDC with fixed step size and compare efficiency favorably against state-of-the-art adaptive RKM.
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Journal of Computational Physics 189(2), 651–675 (2003). https://doi.org/10.1016/S0021-9991(03)00251-1 (4) Layton, A.T., Minion, M.L.: Conservative multi-implicit spectral deferred correction methods for reacting gas dynamics. Journal of Computational Physics 194(2), 697–715 (2004). https://doi.org/10.1016/j.jcp.2003.09.010 (5) Minion, M.L.: Semi-implicit spectral deferred correction methods for ordinary differential equations. Communications in Mathematical Sciences 1(3), 471–500 (2003). https://doi.org/10.4310/CMS.2003.v1.n3.a6 (6) Guo, R., Xu, Y.: High order numerical simulations for the binary fluid–surfactant system using the discontinuous Galerkin and spectral deferred correction methods. SIAM Journal on Scientific Computing 42(2), 353–378 (2020). https://doi.org/10.1137/18M1235405 (7) Feng, X., Tang, T., Yang, J.: Long time numerical simulations for phase-field problems using p𝑝pitalic_p-adaptive spectral deferred correction methods. SIAM Journal on Scientific Computing 37(1), 271–294 (2015). https://doi.org/10.1137/130928662 (8) Quaife, B., Biros, G.: Adaptive time stepping for vesicle suspensions. Journal of Computational Physics 306, 478–499 (2016). https://doi.org/10.1016/j.jcp.2015.11.050 (9) Guo, R., Xu, Y.: A high order adaptive time-stepping strategy and local discontinuous Galerkin method for the modified phase field crystal equation. Communications in Computational Physics 24(1), 123–151 (2018). https://doi.org/10.4208/cicp.OA-2017-0074 (10) Gander, M.J.: 50 years of time parallel time integration. In: Carraro, T., Geiger, M., Körkel, S., Rannacher, R. (eds.) Multiple Shooting and Time Domain Decomposition Methods vol. 9, pp. 69–113. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-23321-5_3. Series Title: Contributions in Mathematical and Computational Sciences (11) Speck, R.: Parallelizing spectral deferred corrections across the method. Computing and Visualization in Science 19(3), 75–83 (2018). https://doi.org/10.1007/s00791-018-0298-x (12) Emmett, M., Minion, M.: Toward an efficient parallel in time method for partial differential equations. Communications in Applied Mathematics and Computational Science 7(1), 105–132 (2012). https://doi.org/10.2140/camcos.2012.7.105 (13) Maday, Y., Mula, O.: An adaptive parareal algorithm. Journal of Computational and Applied Mathematics 377, 112915 (2020). https://doi.org/10.1016/j.cam.2020.112915 (14) Legoll, F., Lelièvre, T., Sharma, U.: An adaptive Parareal algorithm: Application to the simulation of molecular dynamics trajectories. SIAM Journal on Scientific Computing 44(1), 146–176 (2022). https://doi.org/10.1137/21m1412979 (15) Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. 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(eds.) Multiple Shooting and Time Domain Decomposition Methods vol. 9, pp. 69–113. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-23321-5_3. Series Title: Contributions in Mathematical and Computational Sciences (11) Speck, R.: Parallelizing spectral deferred corrections across the method. Computing and Visualization in Science 19(3), 75–83 (2018). https://doi.org/10.1007/s00791-018-0298-x (12) Emmett, M., Minion, M.: Toward an efficient parallel in time method for partial differential equations. Communications in Applied Mathematics and Computational Science 7(1), 105–132 (2012). https://doi.org/10.2140/camcos.2012.7.105 (13) Maday, Y., Mula, O.: An adaptive parareal algorithm. Journal of Computational and Applied Mathematics 377, 112915 (2020). https://doi.org/10.1016/j.cam.2020.112915 (14) Legoll, F., Lelièvre, T., Sharma, U.: An adaptive Parareal algorithm: Application to the simulation of molecular dynamics trajectories. 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Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. 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In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Gander, M.J.: 50 years of time parallel time integration. In: Carraro, T., Geiger, M., Körkel, S., Rannacher, R. (eds.) Multiple Shooting and Time Domain Decomposition Methods vol. 9, pp. 69–113. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-23321-5_3. Series Title: Contributions in Mathematical and Computational Sciences (11) Speck, R.: Parallelizing spectral deferred corrections across the method. Computing and Visualization in Science 19(3), 75–83 (2018). https://doi.org/10.1007/s00791-018-0298-x (12) Emmett, M., Minion, M.: Toward an efficient parallel in time method for partial differential equations. Communications in Applied Mathematics and Computational Science 7(1), 105–132 (2012). https://doi.org/10.2140/camcos.2012.7.105 (13) Maday, Y., Mula, O.: An adaptive parareal algorithm. Journal of Computational and Applied Mathematics 377, 112915 (2020). https://doi.org/10.1016/j.cam.2020.112915 (14) Legoll, F., Lelièvre, T., Sharma, U.: An adaptive Parareal algorithm: Application to the simulation of molecular dynamics trajectories. SIAM Journal on Scientific Computing 44(1), 146–176 (2022). https://doi.org/10.1137/21m1412979 (15) Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. 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In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Parallelizing spectral deferred corrections across the method. Computing and Visualization in Science 19(3), 75–83 (2018). https://doi.org/10.1007/s00791-018-0298-x (12) Emmett, M., Minion, M.: Toward an efficient parallel in time method for partial differential equations. Communications in Applied Mathematics and Computational Science 7(1), 105–132 (2012). https://doi.org/10.2140/camcos.2012.7.105 (13) Maday, Y., Mula, O.: An adaptive parareal algorithm. Journal of Computational and Applied Mathematics 377, 112915 (2020). https://doi.org/10.1016/j.cam.2020.112915 (14) Legoll, F., Lelièvre, T., Sharma, U.: An adaptive Parareal algorithm: Application to the simulation of molecular dynamics trajectories. SIAM Journal on Scientific Computing 44(1), 146–176 (2022). https://doi.org/10.1137/21m1412979 (15) Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. 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SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Emmett, M., Minion, M.: Toward an efficient parallel in time method for partial differential equations. Communications in Applied Mathematics and Computational Science 7(1), 105–132 (2012). https://doi.org/10.2140/camcos.2012.7.105 (13) Maday, Y., Mula, O.: An adaptive parareal algorithm. Journal of Computational and Applied Mathematics 377, 112915 (2020). https://doi.org/10.1016/j.cam.2020.112915 (14) Legoll, F., Lelièvre, T., Sharma, U.: An adaptive Parareal algorithm: Application to the simulation of molecular dynamics trajectories. SIAM Journal on Scientific Computing 44(1), 146–176 (2022). https://doi.org/10.1137/21m1412979 (15) Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. 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Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Maday, Y., Mula, O.: An adaptive parareal algorithm. Journal of Computational and Applied Mathematics 377, 112915 (2020). https://doi.org/10.1016/j.cam.2020.112915 (14) Legoll, F., Lelièvre, T., Sharma, U.: An adaptive Parareal algorithm: Application to the simulation of molecular dynamics trajectories. SIAM Journal on Scientific Computing 44(1), 146–176 (2022). https://doi.org/10.1137/21m1412979 (15) Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Legoll, F., Lelièvre, T., Sharma, U.: An adaptive Parareal algorithm: Application to the simulation of molecular dynamics trajectories. SIAM Journal on Scientific Computing 44(1), 146–176 (2022). https://doi.org/10.1137/21m1412979 (15) Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. 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In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. 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In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. 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Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. 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National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. 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In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. 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In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. 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In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. 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Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Emmett, M., Minion, M.: Toward an efficient parallel in time method for partial differential equations. Communications in Applied Mathematics and Computational Science 7(1), 105–132 (2012). https://doi.org/10.2140/camcos.2012.7.105 (13) Maday, Y., Mula, O.: An adaptive parareal algorithm. Journal of Computational and Applied Mathematics 377, 112915 (2020). https://doi.org/10.1016/j.cam.2020.112915 (14) Legoll, F., Lelièvre, T., Sharma, U.: An adaptive Parareal algorithm: Application to the simulation of molecular dynamics trajectories. SIAM Journal on Scientific Computing 44(1), 146–176 (2022). https://doi.org/10.1137/21m1412979 (15) Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Maday, Y., Mula, O.: An adaptive parareal algorithm. Journal of Computational and Applied Mathematics 377, 112915 (2020). https://doi.org/10.1016/j.cam.2020.112915 (14) Legoll, F., Lelièvre, T., Sharma, U.: An adaptive Parareal algorithm: Application to the simulation of molecular dynamics trajectories. SIAM Journal on Scientific Computing 44(1), 146–176 (2022). https://doi.org/10.1137/21m1412979 (15) Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. 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In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Legoll, F., Lelièvre, T., Sharma, U.: An adaptive Parareal algorithm: Application to the simulation of molecular dynamics trajectories. SIAM Journal on Scientific Computing 44(1), 146–176 (2022). https://doi.org/10.1137/21m1412979 (15) Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. 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In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. 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The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. 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SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. 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Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. 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Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. 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The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. 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Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. 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Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. 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In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Parallelizing spectral deferred corrections across the method. Computing and Visualization in Science 19(3), 75–83 (2018). https://doi.org/10.1007/s00791-018-0298-x (12) Emmett, M., Minion, M.: Toward an efficient parallel in time method for partial differential equations. 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SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. 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In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Emmett, M., Minion, M.: Toward an efficient parallel in time method for partial differential equations. Communications in Applied Mathematics and Computational Science 7(1), 105–132 (2012). https://doi.org/10.2140/camcos.2012.7.105 (13) Maday, Y., Mula, O.: An adaptive parareal algorithm. Journal of Computational and Applied Mathematics 377, 112915 (2020). https://doi.org/10.1016/j.cam.2020.112915 (14) Legoll, F., Lelièvre, T., Sharma, U.: An adaptive Parareal algorithm: Application to the simulation of molecular dynamics trajectories. SIAM Journal on Scientific Computing 44(1), 146–176 (2022). https://doi.org/10.1137/21m1412979 (15) Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. 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SIAM Journal on Scientific Computing 44(1), 146–176 (2022). https://doi.org/10.1137/21m1412979 (15) Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. 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Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. 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Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. 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Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. 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Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. 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Journal of Computational Physics 306, 478–499 (2016). https://doi.org/10.1016/j.jcp.2015.11.050 (9) Guo, R., Xu, Y.: A high order adaptive time-stepping strategy and local discontinuous Galerkin method for the modified phase field crystal equation. Communications in Computational Physics 24(1), 123–151 (2018). https://doi.org/10.4208/cicp.OA-2017-0074 (10) Gander, M.J.: 50 years of time parallel time integration. In: Carraro, T., Geiger, M., Körkel, S., Rannacher, R. (eds.) Multiple Shooting and Time Domain Decomposition Methods vol. 9, pp. 69–113. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-23321-5_3. Series Title: Contributions in Mathematical and Computational Sciences (11) Speck, R.: Parallelizing spectral deferred corrections across the method. Computing and Visualization in Science 19(3), 75–83 (2018). https://doi.org/10.1007/s00791-018-0298-x (12) Emmett, M., Minion, M.: Toward an efficient parallel in time method for partial differential equations. 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The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. 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Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. 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(eds.) Multiple Shooting and Time Domain Decomposition Methods vol. 9, pp. 69–113. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-23321-5_3. Series Title: Contributions in Mathematical and Computational Sciences (11) Speck, R.: Parallelizing spectral deferred corrections across the method. Computing and Visualization in Science 19(3), 75–83 (2018). https://doi.org/10.1007/s00791-018-0298-x (12) Emmett, M., Minion, M.: Toward an efficient parallel in time method for partial differential equations. Communications in Applied Mathematics and Computational Science 7(1), 105–132 (2012). https://doi.org/10.2140/camcos.2012.7.105 (13) Maday, Y., Mula, O.: An adaptive parareal algorithm. Journal of Computational and Applied Mathematics 377, 112915 (2020). https://doi.org/10.1016/j.cam.2020.112915 (14) Legoll, F., Lelièvre, T., Sharma, U.: An adaptive Parareal algorithm: Application to the simulation of molecular dynamics trajectories. 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The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. 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Series Title: Contributions in Mathematical and Computational Sciences (11) Speck, R.: Parallelizing spectral deferred corrections across the method. Computing and Visualization in Science 19(3), 75–83 (2018). https://doi.org/10.1007/s00791-018-0298-x (12) Emmett, M., Minion, M.: Toward an efficient parallel in time method for partial differential equations. Communications in Applied Mathematics and Computational Science 7(1), 105–132 (2012). https://doi.org/10.2140/camcos.2012.7.105 (13) Maday, Y., Mula, O.: An adaptive parareal algorithm. Journal of Computational and Applied Mathematics 377, 112915 (2020). https://doi.org/10.1016/j.cam.2020.112915 (14) Legoll, F., Lelièvre, T., Sharma, U.: An adaptive Parareal algorithm: Application to the simulation of molecular dynamics trajectories. SIAM Journal on Scientific Computing 44(1), 146–176 (2022). https://doi.org/10.1137/21m1412979 (15) Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. 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In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Parallelizing spectral deferred corrections across the method. Computing and Visualization in Science 19(3), 75–83 (2018). https://doi.org/10.1007/s00791-018-0298-x (12) Emmett, M., Minion, M.: Toward an efficient parallel in time method for partial differential equations. 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The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. 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In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Emmett, M., Minion, M.: Toward an efficient parallel in time method for partial differential equations. Communications in Applied Mathematics and Computational Science 7(1), 105–132 (2012). https://doi.org/10.2140/camcos.2012.7.105 (13) Maday, Y., Mula, O.: An adaptive parareal algorithm. 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The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Maday, Y., Mula, O.: An adaptive parareal algorithm. Journal of Computational and Applied Mathematics 377, 112915 (2020). https://doi.org/10.1016/j.cam.2020.112915 (14) Legoll, F., Lelièvre, T., Sharma, U.: An adaptive Parareal algorithm: Application to the simulation of molecular dynamics trajectories. SIAM Journal on Scientific Computing 44(1), 146–176 (2022). https://doi.org/10.1137/21m1412979 (15) Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Legoll, F., Lelièvre, T., Sharma, U.: An adaptive Parareal algorithm: Application to the simulation of molecular dynamics trajectories. SIAM Journal on Scientific Computing 44(1), 146–176 (2022). https://doi.org/10.1137/21m1412979 (15) Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. 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The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. 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Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. 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Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. 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Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. 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Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. 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Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. 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In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Parallelizing spectral deferred corrections across the method. Computing and Visualization in Science 19(3), 75–83 (2018). https://doi.org/10.1007/s00791-018-0298-x (12) Emmett, M., Minion, M.: Toward an efficient parallel in time method for partial differential equations. 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SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. 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In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Emmett, M., Minion, M.: Toward an efficient parallel in time method for partial differential equations. Communications in Applied Mathematics and Computational Science 7(1), 105–132 (2012). https://doi.org/10.2140/camcos.2012.7.105 (13) Maday, Y., Mula, O.: An adaptive parareal algorithm. Journal of Computational and Applied Mathematics 377, 112915 (2020). https://doi.org/10.1016/j.cam.2020.112915 (14) Legoll, F., Lelièvre, T., Sharma, U.: An adaptive Parareal algorithm: Application to the simulation of molecular dynamics trajectories. SIAM Journal on Scientific Computing 44(1), 146–176 (2022). https://doi.org/10.1137/21m1412979 (15) Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. 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SIAM Journal on Scientific Computing 44(1), 146–176 (2022). https://doi.org/10.1137/21m1412979 (15) Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. 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Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. 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Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. 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Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. 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Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. 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(eds.) Multiple Shooting and Time Domain Decomposition Methods vol. 9, pp. 69–113. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-23321-5_3. Series Title: Contributions in Mathematical and Computational Sciences (11) Speck, R.: Parallelizing spectral deferred corrections across the method. Computing and Visualization in Science 19(3), 75–83 (2018). https://doi.org/10.1007/s00791-018-0298-x (12) Emmett, M., Minion, M.: Toward an efficient parallel in time method for partial differential equations. Communications in Applied Mathematics and Computational Science 7(1), 105–132 (2012). https://doi.org/10.2140/camcos.2012.7.105 (13) Maday, Y., Mula, O.: An adaptive parareal algorithm. Journal of Computational and Applied Mathematics 377, 112915 (2020). https://doi.org/10.1016/j.cam.2020.112915 (14) Legoll, F., Lelièvre, T., Sharma, U.: An adaptive Parareal algorithm: Application to the simulation of molecular dynamics trajectories. 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Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. 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Series Title: Contributions in Mathematical and Computational Sciences (11) Speck, R.: Parallelizing spectral deferred corrections across the method. Computing and Visualization in Science 19(3), 75–83 (2018). https://doi.org/10.1007/s00791-018-0298-x (12) Emmett, M., Minion, M.: Toward an efficient parallel in time method for partial differential equations. Communications in Applied Mathematics and Computational Science 7(1), 105–132 (2012). https://doi.org/10.2140/camcos.2012.7.105 (13) Maday, Y., Mula, O.: An adaptive parareal algorithm. Journal of Computational and Applied Mathematics 377, 112915 (2020). https://doi.org/10.1016/j.cam.2020.112915 (14) Legoll, F., Lelièvre, T., Sharma, U.: An adaptive Parareal algorithm: Application to the simulation of molecular dynamics trajectories. 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The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. 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Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. 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Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Parallelizing spectral deferred corrections across the method. Computing and Visualization in Science 19(3), 75–83 (2018). https://doi.org/10.1007/s00791-018-0298-x (12) Emmett, M., Minion, M.: Toward an efficient parallel in time method for partial differential equations. Communications in Applied Mathematics and Computational Science 7(1), 105–132 (2012). https://doi.org/10.2140/camcos.2012.7.105 (13) Maday, Y., Mula, O.: An adaptive parareal algorithm. Journal of Computational and Applied Mathematics 377, 112915 (2020). https://doi.org/10.1016/j.cam.2020.112915 (14) Legoll, F., Lelièvre, T., Sharma, U.: An adaptive Parareal algorithm: Application to the simulation of molecular dynamics trajectories. SIAM Journal on Scientific Computing 44(1), 146–176 (2022). https://doi.org/10.1137/21m1412979 (15) Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. 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The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. 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Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. 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Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. 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Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. 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The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. 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Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. 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Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. 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Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Emmett, M., Minion, M.: Toward an efficient parallel in time method for partial differential equations. Communications in Applied Mathematics and Computational Science 7(1), 105–132 (2012). https://doi.org/10.2140/camcos.2012.7.105 (13) Maday, Y., Mula, O.: An adaptive parareal algorithm. Journal of Computational and Applied Mathematics 377, 112915 (2020). https://doi.org/10.1016/j.cam.2020.112915 (14) Legoll, F., Lelièvre, T., Sharma, U.: An adaptive Parareal algorithm: Application to the simulation of molecular dynamics trajectories. SIAM Journal on Scientific Computing 44(1), 146–176 (2022). https://doi.org/10.1137/21m1412979 (15) Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. 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Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Maday, Y., Mula, O.: An adaptive parareal algorithm. Journal of Computational and Applied Mathematics 377, 112915 (2020). https://doi.org/10.1016/j.cam.2020.112915 (14) Legoll, F., Lelièvre, T., Sharma, U.: An adaptive Parareal algorithm: Application to the simulation of molecular dynamics trajectories. SIAM Journal on Scientific Computing 44(1), 146–176 (2022). https://doi.org/10.1137/21m1412979 (15) Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. 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In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Legoll, F., Lelièvre, T., Sharma, U.: An adaptive Parareal algorithm: Application to the simulation of molecular dynamics trajectories. SIAM Journal on Scientific Computing 44(1), 146–176 (2022). https://doi.org/10.1137/21m1412979 (15) Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. 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Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. 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In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. 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Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. 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The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. 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Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. 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SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. 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Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. 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In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Gander, M.J.: 50 years of time parallel time integration. In: Carraro, T., Geiger, M., Körkel, S., Rannacher, R. (eds.) Multiple Shooting and Time Domain Decomposition Methods vol. 9, pp. 69–113. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-23321-5_3. Series Title: Contributions in Mathematical and Computational Sciences (11) Speck, R.: Parallelizing spectral deferred corrections across the method. Computing and Visualization in Science 19(3), 75–83 (2018). https://doi.org/10.1007/s00791-018-0298-x (12) Emmett, M., Minion, M.: Toward an efficient parallel in time method for partial differential equations. Communications in Applied Mathematics and Computational Science 7(1), 105–132 (2012). https://doi.org/10.2140/camcos.2012.7.105 (13) Maday, Y., Mula, O.: An adaptive parareal algorithm. Journal of Computational and Applied Mathematics 377, 112915 (2020). https://doi.org/10.1016/j.cam.2020.112915 (14) Legoll, F., Lelièvre, T., Sharma, U.: An adaptive Parareal algorithm: Application to the simulation of molecular dynamics trajectories. SIAM Journal on Scientific Computing 44(1), 146–176 (2022). https://doi.org/10.1137/21m1412979 (15) Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. 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Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. 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Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Parallelizing spectral deferred corrections across the method. Computing and Visualization in Science 19(3), 75–83 (2018). https://doi.org/10.1007/s00791-018-0298-x (12) Emmett, M., Minion, M.: Toward an efficient parallel in time method for partial differential equations. Communications in Applied Mathematics and Computational Science 7(1), 105–132 (2012). https://doi.org/10.2140/camcos.2012.7.105 (13) Maday, Y., Mula, O.: An adaptive parareal algorithm. Journal of Computational and Applied Mathematics 377, 112915 (2020). https://doi.org/10.1016/j.cam.2020.112915 (14) Legoll, F., Lelièvre, T., Sharma, U.: An adaptive Parareal algorithm: Application to the simulation of molecular dynamics trajectories. SIAM Journal on Scientific Computing 44(1), 146–176 (2022). https://doi.org/10.1137/21m1412979 (15) Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. 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In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Emmett, M., Minion, M.: Toward an efficient parallel in time method for partial differential equations. Communications in Applied Mathematics and Computational Science 7(1), 105–132 (2012). https://doi.org/10.2140/camcos.2012.7.105 (13) Maday, Y., Mula, O.: An adaptive parareal algorithm. Journal of Computational and Applied Mathematics 377, 112915 (2020). https://doi.org/10.1016/j.cam.2020.112915 (14) Legoll, F., Lelièvre, T., Sharma, U.: An adaptive Parareal algorithm: Application to the simulation of molecular dynamics trajectories. SIAM Journal on Scientific Computing 44(1), 146–176 (2022). https://doi.org/10.1137/21m1412979 (15) Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. 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In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Maday, Y., Mula, O.: An adaptive parareal algorithm. Journal of Computational and Applied Mathematics 377, 112915 (2020). https://doi.org/10.1016/j.cam.2020.112915 (14) Legoll, F., Lelièvre, T., Sharma, U.: An adaptive Parareal algorithm: Application to the simulation of molecular dynamics trajectories. 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The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. 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Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. 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Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. 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SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Legoll, F., Lelièvre, T., Sharma, U.: An adaptive Parareal algorithm: Application to the simulation of molecular dynamics trajectories. SIAM Journal on Scientific Computing 44(1), 146–176 (2022). https://doi.org/10.1137/21m1412979 (15) Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. 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The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. 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SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. 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Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. 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SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. 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The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. 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SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. 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SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Legoll, F., Lelièvre, T., Sharma, U.: An adaptive Parareal algorithm: Application to the simulation of molecular dynamics trajectories. SIAM Journal on Scientific Computing 44(1), 146–176 (2022). https://doi.org/10.1137/21m1412979 (15) Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. 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In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. 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SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. 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SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Parallelizing spectral deferred corrections across the method. Computing and Visualization in Science 19(3), 75–83 (2018). https://doi.org/10.1007/s00791-018-0298-x (12) Emmett, M., Minion, M.: Toward an efficient parallel in time method for partial differential equations. Communications in Applied Mathematics and Computational Science 7(1), 105–132 (2012). https://doi.org/10.2140/camcos.2012.7.105 (13) Maday, Y., Mula, O.: An adaptive parareal algorithm. Journal of Computational and Applied Mathematics 377, 112915 (2020). https://doi.org/10.1016/j.cam.2020.112915 (14) Legoll, F., Lelièvre, T., Sharma, U.: An adaptive Parareal algorithm: Application to the simulation of molecular dynamics trajectories. SIAM Journal on Scientific Computing 44(1), 146–176 (2022). https://doi.org/10.1137/21m1412979 (15) Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. 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Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. 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Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Emmett, M., Minion, M.: Toward an efficient parallel in time method for partial differential equations. Communications in Applied Mathematics and Computational Science 7(1), 105–132 (2012). https://doi.org/10.2140/camcos.2012.7.105 (13) Maday, Y., Mula, O.: An adaptive parareal algorithm. Journal of Computational and Applied Mathematics 377, 112915 (2020). https://doi.org/10.1016/j.cam.2020.112915 (14) Legoll, F., Lelièvre, T., Sharma, U.: An adaptive Parareal algorithm: Application to the simulation of molecular dynamics trajectories. SIAM Journal on Scientific Computing 44(1), 146–176 (2022). https://doi.org/10.1137/21m1412979 (15) Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. 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SIAM Journal on Scientific Computing 44(1), 146–176 (2022). https://doi.org/10.1137/21m1412979 (15) Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. 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Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. 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Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. 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Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. 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Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. 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Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. 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Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Emmett, M., Minion, M.: Toward an efficient parallel in time method for partial differential equations. Communications in Applied Mathematics and Computational Science 7(1), 105–132 (2012). https://doi.org/10.2140/camcos.2012.7.105 (13) Maday, Y., Mula, O.: An adaptive parareal algorithm. Journal of Computational and Applied Mathematics 377, 112915 (2020). https://doi.org/10.1016/j.cam.2020.112915 (14) Legoll, F., Lelièvre, T., Sharma, U.: An adaptive Parareal algorithm: Application to the simulation of molecular dynamics trajectories. SIAM Journal on Scientific Computing 44(1), 146–176 (2022). https://doi.org/10.1137/21m1412979 (15) Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. 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SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. 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Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Maday, Y., Mula, O.: An adaptive parareal algorithm. Journal of Computational and Applied Mathematics 377, 112915 (2020). https://doi.org/10.1016/j.cam.2020.112915 (14) Legoll, F., Lelièvre, T., Sharma, U.: An adaptive Parareal algorithm: Application to the simulation of molecular dynamics trajectories. SIAM Journal on Scientific Computing 44(1), 146–176 (2022). https://doi.org/10.1137/21m1412979 (15) Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Legoll, F., Lelièvre, T., Sharma, U.: An adaptive Parareal algorithm: Application to the simulation of molecular dynamics trajectories. SIAM Journal on Scientific Computing 44(1), 146–176 (2022). https://doi.org/10.1137/21m1412979 (15) Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. 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National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. 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National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. 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SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. 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In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. 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Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1
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The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. 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Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Maday, Y., Mula, O.: An adaptive parareal algorithm. Journal of Computational and Applied Mathematics 377, 112915 (2020). https://doi.org/10.1016/j.cam.2020.112915 (14) Legoll, F., Lelièvre, T., Sharma, U.: An adaptive Parareal algorithm: Application to the simulation of molecular dynamics trajectories. 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The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Legoll, F., Lelièvre, T., Sharma, U.: An adaptive Parareal algorithm: Application to the simulation of molecular dynamics trajectories. SIAM Journal on Scientific Computing 44(1), 146–176 (2022). https://doi.org/10.1137/21m1412979 (15) Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. 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Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. 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Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. 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Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Legoll, F., Lelièvre, T., Sharma, U.: An adaptive Parareal algorithm: Application to the simulation of molecular dynamics trajectories. SIAM Journal on Scientific Computing 44(1), 146–176 (2022). https://doi.org/10.1137/21m1412979 (15) Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. 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Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. 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Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kazakov, E., Efremenko, D., Zemlyakov, V., Gao, J.: A time-parallel ordinary differential equation solver with an adaptive step size: Performance assessment. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds.) Supercomputing, pp. 3–17. Springer, Cham (2022) (16) Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. 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Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. The International Journal of High Performance Computing Applications 29(4), 403–421 (2015). https://doi.org/10.1177/1094342014532297 (17) Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. 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Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. 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The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. 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Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. 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In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1
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In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Benson, A.R., Schmit, S., Schreiber, R.: Silent error detection in numerical time-stepping schemes. 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The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. 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Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. 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Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1
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Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L., Benacchio, T., Bonaventura, L., Bungartz, H.-J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Ortí, E.S., Rizzi, F., Rüde, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A., Wohlmuth, B.: Resiliency in numerical algorithm design for extreme scale simulations. The International Journal of High Performance Computing Applications 36(2), 251–285 (2022). https://doi.org/10.1177/10943420211055188 (18) Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. 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Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. 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Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. 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Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guhur, P.-L., Zhang, H., Peterka, T., Constantinescu, E., Cappello, F.: Lightweight and accurate silent data corruption detection in ordinary differential equation solvers. In: Dutot, P.-F., Trystram, D. (eds.) Euro-Par 2016: Parallel Processing, pp. 644–656. Springer, Cham (2016) (19) Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. 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Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) 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SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. 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The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. 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Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1
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In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Berrut, J.-P., Trefethen, L.N.: Barycentric Lagrange interpolation. SIAM Review 46(3), 501–517 (2004). https://doi.org/10.1137/S0036144502417715 (20) Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. 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In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. 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Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-05221-7. http://link.springer.com/10.1007/978-3-642-05221-7 (21) Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. 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Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1
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In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. 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The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. 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In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. 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Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. 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The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. 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Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1
- Christlieb, A., Ong, B., Qiu, J.-M.: Integral deferred correction methods constructed with high order Runge–Kutta integrators. Mathematics of Computation 79(270), 761–783 (2009). https://doi.org/10.1090/S0025-5718-09-02276-5 (22) Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Ong, B., Qiu, J.-M.: Comments on high-order integrators embedded within integral deferred correction methods. Communications in Applied Mathematics and Computational Science 4(1), 27–56 (2009). https://doi.org/10.2140/camcos.2009.4.27 (23) Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. 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The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Causley, M., Seal, D.: On the convergence of spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 14(1), 33–64 (2019). https://doi.org/10.2140/camcos.2019.14.33 (24) Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. 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SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1
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Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M.: Faster SDC convergence on non-equidistant grids by DIRK sweeps. BIT Numerical Mathematics 55(4), 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y (25) Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. 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SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kremling, G., Speck, R.: Convergence of multilevel spectral deferred corrections. Communications in Applied Mathematics and Computational Science 16(2), 227–265 (2021) (26) Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. 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In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. 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Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. 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National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. 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In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. 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Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schöbel, R., Speck, R.: PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science 23(1-4), 12 (2020). https://doi.org/10.1007/s00791-020-00330-5 (27) Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. 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SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. 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Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1
- Čaklović, G., Lunet, T., Götschel, S., Ruprecht, D.: Improving parallelism accross the method for spectral deferred correction (2024). in preparation (28) Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. 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The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1
- Freese, P., Götschel, S., Lunet, T., Ruprecht, D., Schreiber, M.: Parallel performance of shared memory parallel spectral deferred corrections (2024). in preparation (29) Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Dickopf, T., Gander, M.J., Halpern, L., Krause, R., Pavarino, L.F. (eds.) Domain Decomposition Methods in Science and Engineering XXII, pp. 389–396. Springer, Cham (2016) (30) Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. 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Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. 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SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Ghosh, S.: Theoretically optimal inexact spectral deferred correction methods. Communications in Applied Mathematics and Computational Science 13(1), 53–86 (2018). https://doi.org/10.2140/camcos.2018.13.53 (31) Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. 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SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guesmi, M., Grotteschi, M., Stiller, J.: Assessment of high-order IMEX methods for incompressible flow. International Journal for Numerical Methods in Fluids 95(6), 954–978 (2023) https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5177. https://doi.org/10.1002/fld.5177 (32) Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. 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Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) 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In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. 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Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1
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In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Hairer, E., Wanner, G., Nørsett, S.P.: Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin, Heidelberg (1993). https://doi.org/10.1007/978-3-540-78862-1 (33) Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. 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SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. 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Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. 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Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. 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In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Tsitouras, C.: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications 62(2), 770–775 (2011). https://doi.org/10.1016/j.camwa.2011.06.002 (34) Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Huang, J., Jia, J., Minion, M.: Accelerating the convergence of spectral deferred correction methods. Journal of Computational Physics 214(2), 633–656 (2006). https://doi.org/10.1016/j.jcp.2005.10.004 (35) Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. 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Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. 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Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. 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The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. 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In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. 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National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. 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Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. 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National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. 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In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. 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SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. 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Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics 45(2), 341–373 (2005). https://doi.org/10.1007/s10543-005-0016-1 (36) Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. 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SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1
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SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guibert, D., Tromeur-Dervout, D.: Parallel deferred correction method for CFD problems. In: Kwon, J.H., Ecer, A., Satofuka, N., Periaux, J., Fox, P. (eds.) Parallel Computational Fluid Dynamics 2006, pp. 131–138. Elsevier Science B.V., Amsterdam (2007). https://doi.org/10.1016/B978-044453035-6/50019-5 (37) Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. 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Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. 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Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1
- Christlieb, A.J., Macdonald, C.B., Ong, B.W.: Parallel high-order integrators. SIAM Journal on Scientific Computing 32(2), 818–835 (2010). https://doi.org/10.1137/09075740X (38) Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. 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Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1
- Gander, M.J., Lunet, T., Ruprecht, D., Speck, R.: A unified analysis framework for iterative parallel-in-time algorithms. SIAM Journal on Scientific Computing 45(5), 2275–2303 (2023). https://doi.org/10.1137/22M1487163 (39) Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schroeder, B., Pinheiro, E., Weber, W.-D.: DRAM errors in the wild: A large-scale field study. Commun. ACM 54(2), 100–107 (2011). https://doi.org/10.1145/1897816.1897844 (40) Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. 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In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. 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In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. 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In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1
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National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Lapinsky, S.E., Easty, A.C.: Electromagnetic interference in critical care. Journal of Critical Care 21(3), 267–270 (2006). https://doi.org/10.1016/j.jcrc.2006.03.010 (41) Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1
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Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Glosli, J.N., Richards, D.F., Caspersen, K.J., Rudd, R.E., Gunnels, J.A., Streitz, F.H.: Extending stability beyond CPU millennium: A micron-scale atomistic simulation of Kelvin-Helmholtz instability. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. SC ’07. Association for Computing Machinery, New York, NY, USA (2007). https://doi.org/10.1145/1362622.1362700. https://doi.org/10.1145/1362622.1362700 (42) Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1
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The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. 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Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Guerraoui, R., Schiper, A.: Software-based replication for fault tolerance. Computer 30(4), 68–74 (1997). https://doi.org/10.1109/2.585156 (43) Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. 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In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. 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Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. 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National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. 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In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. 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In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. 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Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. 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Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1
- Cappello, F., Di, S., Li, S., Liang, X., Gok, A.M., Tao, D., Yoon, C.H., Wu, X.-C., Alexeev, Y., Chong, F.T.: Use cases of lossy compression for floating-point data in scientific data sets. The International Journal of High Performance Computing Applications 33(6), 1201–1220 (2019). https://doi.org/10.1177/1094342019853336 (44) Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Grout, R., Kolla, H., Minion, M., Bell, J.: Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Communications in Applied Mathematics and Computational Science 12(1), 25–50 (2017). https://doi.org/10.2140/camcos.2017.12.25 (45) Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. 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Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1
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Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. 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Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1
- Cash, J.R., Karp, A.H.: A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software 16(3), 201–222 (1990). https://doi.org/10.1145/79505.79507 (46) Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. 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Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Wei, J., Thomas, A., Li, G., Pattabiraman, K.: Quantifying the accuracy of high-level fault injection techniques for hardware faults. In: 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pp. 375–382 (2014). https://doi.org/10.1109/DSN.2014.2 (47) Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1
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The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. 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SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. 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Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1
- Speck, R., Ruprecht, D.: Toward fault-tolerant parallel-in-time integration with pfasst. Parallel Computing 62, 20–37 (2017). https://doi.org/10.1016/j.parco.2016.12.001 (48) Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Speck, R.: Algorithm 997: pySDC—Prototyping spectral deferred corrections. ACM Trans. Math. Softw. 45(3) (2019). https://doi.org/10.1145/3310410 (49) Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1
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In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1
- Von St. Vieth, B.: JUSUF: Modular tier-2 supercomputing and cloud infrastructure at Jülich Supercomputing Centre. Journal of large-scale research facilities JLSRF 7, 179 (2021). https://doi.org/10.17815/jlsrf-7-179 (50) Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. 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Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Van Der Pol, B.: LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11), 978–992 (1926). https://doi.org/10.1080/14786442608564127 (51) van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1
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SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 van der Pol, B.: The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers 22(9), 1051–1086 (1934). https://doi.org/10.1109/JRPROC.1934.226781 (52) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1
- Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17, 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2 (53) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1
- Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980). https://doi.org/10.1016/0771-050X(80)90013-3 (54) Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1
- Schnaubelt, E., Wozniak, M., Schöps, S.: Thermal thin shell approximation towards finite element quench simulation. Superconductor Science and Technology 36(4), 044004 (2023). https://doi.org/10.1088/1361-6668/acbeea (55) Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1
- Bajko, M., Bertinelli, F., Catalan-Lasheras, N., Claudet, S., Cruikshank, P., Dahlerup-Petersen, K., Denz, R., Fessia, P., Garion, C., Jimenez, J., Kirby, G., Lebrun, P., Le Naour, S., Mess, K.-H., Modena, M., Montabonnet, V., Nunes, R., Parma, V., Perin, A., de Rijk, G., Rijllart, A., Rossi, L., Schmidt, R., Siemko, A., Strubin, P., Tavian, L., Thiesen, H., Tock, J., Todesco, E., Veness, R., Verweij, A., Walckiers, L., Van Weelderen, R., Wolf, R., Fehér, S., Flora, R., Koratzinos, M., Limon, P., Strait, J.: Report of the task force on the incident of 19th September 2008 at the LHC. Technical report, CERN, Geneva (2009). https://cds.cern.ch/record/1168025 (56) Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1), 1–22 (1997). https://doi.org/10.1137/S1064827594276424 (57) Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1
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In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1
- Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546709 (58) Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Problems 23(5), 2171 (2007). https://doi.org/10.1088/0266-5611/23/5/021 (59) Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1
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In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1
- Zhang, J., Du, Q.: Numerical studies of discrete approximations to the Allen–Cahn equation in the sharp interface limit. SIAM Journal on Scientific Computing 31(4), 3042–3063 (2009) https://doi.org/10.1137/080738398. https://doi.org/10.1137/080738398 (60) Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1
- Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review. National Aeronautics and Space Administration (2016). https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf (61) Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1
- Kennedy, C.A., Carpenter, M.H.: Higher-order additive Runge–Kutta schemes for ordinary differential equations. Applied Numerical Mathematics 136, 183–205 (2019). https://doi.org/10.1016/j.apnum.2018.10.007 (62) Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1
- Weiser, M., Scacchi, S.: Spectral deferred correction methods for adaptive electro-mechanical coupling in cardiac simulation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321–328. Springer, Cham (2016) (63) Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1
- Weiser, M., Chegini, F.: Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods. In: CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528–531 (2022) (64) Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1
- Chegini, F., Steinke, T., Weiser, M.: Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. arXiv e-prints, 2311–07206 (2023) arXiv:2311.07206 [math.NA]. https://doi.org/10.48550/arXiv.2311.07206 (65) Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1 Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1
- Christlieb, A., Macdonald, C., Ong, B., Spiteri, R.: Revisionist integral deferred correction with adaptive step-size control. Communications in Applied Mathematics and Computational Science 10(1), 1–25 (2015). https://doi.org/10.2140/camcos.2015.10.1